Answer: [MT⁻²] (force per length = energy per area).
- A [MT⁻²] (force per length = energy per area)
- B [MLT⁻²], the dimensional formula for force itself
- C [ML⁻¹T⁻²], the dimensional formula for pressure or stress
- D [ML²T⁻²], the dimensional formula for energy or work
Correct answer: A. [MT⁻²] (force per length = energy per area)
Explanation: T = F/L = [MLT⁻²/L] = [MT⁻²]. Equivalently, energy/area = [ML²T⁻²/L²] = [MT⁻²]. Both confirm the same dimensions.
Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.
Concept context
Pressure, buoyancy, Bernoulli equation, viscosity, and surface tension.